Bitcoins are neither. They neither depend on more people joining,nor is the inherent value of a BTC dependent on newer adopters. These allegations of it being either a pyramid or ponzi scheme stem from the suddenly rising value of it,but that value inflation is due to pure demand-supply equations rather than anything else.
The price of Bitcoin is going up because Bitcoiners are pumping it to get more and more new participants to enter. The media is not helping the situation either with their report of skyrocketing prices. This should be a clue for some people that the Bitcoin scheme is a pyramid scheme.
As you state that Bitcoin can work with no new participants. Can it work?
Let's do a thought experiment.
Assuming:
No new coin creation, it stops now
12 million total BTC supply and it's fixed at 12 million
1 million Bitcoiners
Looking at BTC Distribution.
the Pharaoh (Satoshi) 3m BTC 25%
early adopters, ruling class Lords (~100 people) 2m BTC 17%
early adopters, ruling class Governors (~2000 people) 1m BTC 8%
early adopters, elite class (~15000 people) 1m BTC 8%
.... it gets granular as we go down, but let's lump the rest together
late adopters, working and slave class (~980000 people) BTC 5m 42%
This is a rough estimate distribution from Bitcoin supply issuance scheme and early adopters were few, maybe under 20000 people.
Teleport the one million Bitcoiners to planet BitEarth.
On BitEarth, let's simplified things and condense time so we can get a better visual. The basic principle is the same.
One generation is one year and population growth doubles every year. Die-offs after 3 generations.
Year - Population
1 - 1m
2 - 2m
3 - 4m
4 - 7m (1m die-off)
5 - 12m (2m die-off)
6 - 20m (4m die-off)
Since money supply is fixed at 12 million BTC, as population grows economic activity grows, the money supply can be increased by moving the decimal point, 0.01 (year 1), 0.001 (year 2) and so on. Over subsequent generations, the wealth gaps incremental widens more and more. The slave class where the majority resides have the widest gap between the ruling class.
This is not how a fair monetary system can possible work.
I hope people can see why the Bitcoin scheme is a pyramid scheme.